A basement or garage range is a good suggestion. Unfortunately, I don't have a basement, and my garage isn't as deep as I'd like but it's better than nothing.
Thought I'd include a partial excerpt from our local laws here in FL which clearly includes airguns with firearms in terms of safe discharge. Other States, counties or local areas may have similar or more restrictive laws:
"No person shall discharge a firearm or air gun within the incorporated area of the city, over, around, through or so near the occupied structures, livestock, pets, chattels or person of another, that might reasonably be expected to do harm, should such persons or objects be struck by any projectiles fired from such firearms or air guns. It is not a requirement of this article that any person or object be struck by a projectile in order for there to be a finding by law enforcement officials or the courts that this section has been violated.
Should any such discharge of a firearm or air gun take place within 150 yards of the occupied structure of another, it shall be prime facie evidence that the persons or person discharging knew that the structure existed and that it was occupied."
YMMV but I would check your local laws and err on the side of caution. I guess a basement or garage range properly set up with a collecting backstop is 'out of sight - out of mind' for neighborly complaints.